藉部分區域穩定理論之 坎-離八卦多重交織導數同步

Abstract

太極為陰陽之結合，而太極渾沌系統即為陽渾沌系統與陰渾沌系統之合併。 陽系統為正數系統，及一般系統，而陰系統則為負數時間之系統。八卦為太極之 延伸，每個卦皆有各自對應的方向、圖形、代表物。八卦同步利用它們各自的圖 形代表三個不同的渾沌系統，接著再用多重交織同步完成八卦同步。六十四卦為 八卦的進階，它分上、下兩部分，這兩部分都代表八卦的一個卦象，而六十四卦 同步即為八卦同步的延伸。同步一般是指系統間存在著主僕般的函數關係。而新 的渾沌多重交織同步則是原來的系統與其他系統間變為伙伴間的函數關係。最後 利用數值模擬來驗證前述計畫。

“Tai Ji”, the great one, is the combination of Yin and Yang, and Tai Ji chaotic system is the combination of “Yang” chaotic system and “Yin” chaotic system. Yang system represents contemporary system, and Yin system means historical system. The eight trigrams, a part of Chinese philosophy, is advance of “Tai Ji”, and they have their own directions, figures, and representations. Trigram synchronization uses three different chaos systems by the figures, and multiple symplectic derivative synchronization is used. Hexagram, advance of the eight trigrams, has two parts, upper and low, which both represent a trigram, and the hexagram synchronization is advance of trigram synchronization. The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new type of chaotic synchronization, multiple chaotic symplectic synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Numerical simulations are provided to verify the effectiveness of the scheme.